How Do Logarithms Solve Real-World Problems?

  • Thread starter Thread starter KrimsonB
  • Start date Start date
  • Tags Tags
    Test
AI Thread Summary
Logarithms are used to solve various real-world problems, such as calculating cooling times of objects, determining pH levels, and measuring earthquake magnitudes. The discussion includes solving the equation 10^(x+3) = 6^(2x) by taking logarithms, leading to a simplified expression for x. Newton's law of cooling is applied to find the time required for a car engine to cool from 190°F to 100°F, given a surrounding temperature of 60°F. Additionally, the relationship between pH and hydrogen ion concentration is explored, demonstrating how to convert pH values into concentrations using logarithmic functions. The conversation emphasizes the importance of correctly interpreting logarithmic equations for accurate problem-solving.
KrimsonB
Messages
1
Reaction score
0
10^ x+3 = 6^2x ?

after i take the log of both sides and evaluating i end up getting -x = -2.22

a car engine runs at a temperature of 190 f when the engine is turned off it cools according to Newtons law of cooling with constant k = 0.0341, where the time is measure in minutes. find the time needed for the engine to cool 90f if the surrounding temp is 60f
T(t)=Ts+Doe^-kt

the ph of lime juice IS 1.9 FIND THE HYDROGEN ION CONCENTRATION

PH= -LOG [H+]

IF ONE EARTHQUAKE HAS A MAGNITUDE OF 6.5 ON THE RICHTER SCALE, WHAT IS THE MAGNITUDE OF ANOTHER QUAKE THAT IS 35 TIMES AS INTENSE?

M=LOG(I\S)

x^2e ^2x + 2xe^2x = 8e^2x
 
Physics news on Phys.org
KrimsonB said:
10^ x+3 = 6^2x ?

after i take the log of both sides and evaluating i end up getting -x = -2.22

I think this may be wrong, you may need to do it over, unless I typed it in my calculator incorrectly.

KrimsonB said:
a car engine runs at a temperature of 190 f when the engine is turned off it cools according to Newtons law of cooling with constant k = 0.0341, where the time is measure in minutes. find the time needed for the engine to cool 90f if the surrounding temp is 60f
T(t)=Ts+Doe^-kt

you need to post your work for this. Start by finding the value of D0

KrimsonB said:
the ph of lime juice IS 1.9 FIND THE HYDROGEN ION CONCENTRATION

PH= -LOG [H+]

So you know that 1.9 = -lg[H+], how would you go about taking anti-logs?

KrimsonB said:
IF ONE EARTHQUAKE HAS A MAGNITUDE OF 6.5 ON THE RICHTER SCALE, WHAT IS THE MAGNITUDE OF ANOTHER QUAKE THAT IS 35 TIMES AS INTENSE?

M=LOG(I\S)[/QUOTE]

I am not sure what I and S are. I assume M meant magnitude.

KrimsonB said:
x^2e ^2x + 2xe^2x = 8e^2x

You can easily solve for x here since e2x is common in every term and will cancel out.
 
KrimsonB said:
10^ x+3 = 6^2x ?

after i take the log of both sides and evaluating i end up getting -x = -2.22
I assume you mean 10^(x+3)= 6^(2x).
Taking logarithms of both sides, x+ 3= 2x(log(6))
(log(6)-1)x= 3.

x clearly is positive.

a car engine runs at a temperature of 190 f when the engine is turned off it cools according to Newtons law of cooling with constant k = 0.0341, where the time is measure in minutes. find the time needed for the engine to cool 90f if the surrounding temp is 60f
T(t)=Ts+Doe^-kt
Well, what do Ts and Do represent?

the ph of lime juice IS 1.9 FIND THE HYDROGEN ION CONCENTRATION

PH= -LOG [H+]
So log[H+]= -PH. [H+]= exp(-PH)

IF ONE EARTHQUAKE HAS A MAGNITUDE OF 6.5 ON THE RICHTER SCALE, WHAT IS THE MAGNITUDE OF ANOTHER QUAKE THAT IS 35 TIMES AS INTENSE?

M=LOG(I\S)
Log(35)

x^2e ^2x + 2xe^2x = 8e^2x
What is the problem? To solve for x? What do you get if you divide the entire equation by e^(2x)?
 
The pH is defined thus: pH = -log (H+ conc.) = log (1/H+ conc.), where log is base ten or common logarithms. Therefore [H+] = 10^(-pH).
 
About 10^ x+3 = 6^2x: if we parse this using the usual rules (exponentiation takes precedence over multiplication), you have written
10^x + 3 = 36*x. If your really mean 10^x + 3 = 6^(2x), you need to include brackets.

RGV
 

Hot Threads

Recent Insights

Back
Top